Flowmeter Calibration Instructions

Congratulations on being hired as an engineer! Listed below are instructions on how to calibrate hydraulic and paddlewheel flowmeters and with a little practice, you will become a master.

Using provided data related to the hydraulic flowmeter, the measured flow rate, on the y-axis, can be plotted with respect to the manometer deflection, on the x-axis, for either a Venturi meter or orifice-plate meter. Once a graph is created with these values, create a power trendline for the dataset which corresponds to a calibration curve for the utilized flowmeter. An example of a calibration curve that I created previously can be found above.

After obtaining the graph in the previous step, the axes values can be formatted to a logarithmic scale. The curve from the previous, linear scale will be adjusted to the new scale and can be considered an alternative calibration curve in comparison to the previous method. The data, as seen in the example above, follows a straight line pattern, indicating the application of the power-law relation which can be formally written through the following equation: Q = K(Δh)^m. This relation signifies a direct relationship between two forms of measurement, but are independent of their initial conditions.

The discharge coefficient, Cd, can be plotted with respect to the Reynolds number, Re, where the discharge coefficient axis has a linear scale while the Reynolds number scale is logarithmic. Both of these values were found through using the full pipe diameter, D, the Reynolds number can be found using the following relation: Re=V1*D/v. V1 is the pipe velocity while v is the viscosity. Furthermore, the discharge coefficient can be found through equation seven listed above where Beta is the quotient of the orifice diameter, d, and full pipe diameter while Q is the flow rate. An example plot can be found above as well.

As seen in step three, the discharge coefficient remained relatively constant throughout the range of Reynold's numbers utilized during experimentation, although this value is not the ideal, theoretical value of one for the discharge coefficient. Instead, it remained at 0.7 which is still relatively close. The reasoning for the difference between the theoretical and experimental values is related to the assumed ideal conditions which are not necessarily true, such as no friction present in the system. Consequently, to obtain more accurate theoretical results, the Reynolds number should decrease as the discharge coefficient increases, as seen in the figure above, which can occur when a smaller flow rate is achieved. Although, if the flow rate is too small, data collection may become a challenge and therefore may not be possible through the experiment completed in this tutorial.

Next, the paddlewheel flowmeter is utilized to produce a voltage that has a proportional relationship with the velocity of the fluid in the pipe along with its corresponding flow rate. The direct connection between the outputted voltage and the actual flow, or discharge, rate can be created as seen above. Separately, rising and cutoff flow rates can be found by looking at the created plot. The point where the data begins to increase vertically and horizontally is the rising flow rate while a cutoff flow rate can be found by looking at a point where the graph begins to decline. Both of these values indicate when the paddlewheel will appear motionless. In the example above, there is a definitive rising flow rate of 0.00316 m^3/s with no cutoff flow rate with a corresponding fluid velocity value of 0.497 meters per second. Additionally, the maximum fluid velocity was found to be 3.160 meters per second.

A paddlewheel flowmeter is a device that has great reliability reflected by its ability to show a desired linear relationship between the voltage output and the actual discharge rate. This was obtained previously with an R^2 value of 0.9995 as seen in step five. Although, in general, the readings related to a paddlewheel flowmeter are not as accurate at both extremely high and low flowrate values. At low flowrates, there would be a considerable amount of friction and resistance that would cause the wheel not to spin. Inversely, higher flow rates would cause the paddlewheel to spin extremely fast and increase the error of a voltage reading.